You upgrade your squad by collecting the gold medals in the missions. You can see whether or not you have the medal in any given mission in the mission select screen. If you collect every medal in the campaign you will have 2 left over so if you miss a couple don't trip. The upgrades cost 3, 3, 4, 4, 5, 5, and 6 medals for a total of 30. Some missions have 2 medals in them so be on the look out. Also if you buy the Intel Pack from the in-mission store for 5,000 points, it will add green dots to your mini-map to show you where the gold medals are.
Price updated thanks to Dragon Weew